Notice that in the progression you gave above (Fighter 3 --> Wizard 2 --> Fighter 7 --> Wizard 4), you don't get second level spells until level 9, two levels behind a single classed EK, and you don't get an ASI until level 6.

Fracking multiclass rules for wizards :/ Somehow I forgot that spell level slots aren't the same as the ability to learn those spells :/